Question: Solve for $x$ and $y$ using substitution. ${-6x-5y = 3}$ ${x = 2y+8}$
Solution: Since $x$ has already been solved for, substitute $2y+8$ for $x$ in the first equation. ${-6}{(2y+8)}{- 5y = 3}$ Simplify and solve for $y$ $-12y-48 - 5y = 3$ $-17y-48 = 3$ $-17y-48{+48} = 3{+48}$ $-17y = 51$ $\dfrac{-17y}{{-17}} = \dfrac{51}{{-17}}$ ${y = -3}$ Now that you know ${y = -3}$ , plug it back into $\thinspace {x = 2y+8}\thinspace$ to find $x$ ${x = 2}{(-3)}{ + 8}$ $x = -6 + 8$ ${x = 2}$ You can also plug ${y = -3}$ into $\thinspace {-6x-5y = 3}\thinspace$ and get the same answer for $x$ : ${-6x - 5}{(-3)}{= 3}$ ${x = 2}$